PROOUT - Revision history

Schlipf at 13:33, 7 March 2025

2025-03-07T13:33:20Z

← Older revision		Revision as of 13:33, 7 March 2025
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	----		----

	[[Category:Files]][[Category:Output ~~Files~~]]		[[Category:Files]][[Category:Output files]]

Miranda.henrique at 15:02, 17 August 2022

2022-08-17T15:02:45Z

← Older revision		Revision as of 15:02, 17 August 2022
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	</math>		</math>

	The spherical bessel functions <math>\phi_n(r)</math> are parametrized to be non-zero within a radius determined by {{TAG\|RWIGS}}. In addition, it so happens that <math>\|~~p_i~~\rangle</math> has a similar form as <math>\|\beta^\alpha_{lm}\rangle</math> which simplifies the computations above.		The spherical bessel functions <math>\phi_n(r)</math> are parametrized to be non-zero within a radius determined by {{TAG\|RWIGS}}. In addition, it so happens that <math>\|\tilde{p}_i\rangle</math> has a similar form as <math>\|\beta^\alpha_{lm}\rangle</math> which simplifies the computations above.

	The {{TAG\|PROOUT}} file contains similar information as the {{TAG\|PROCAR}} file but the following differences exist:		The {{TAG\|PROOUT}} file contains similar information as the {{TAG\|PROCAR}} file but the following differences exist:

Miranda.henrique at 15:02, 17 August 2022

2022-08-17T15:02:25Z

← Older revision		Revision as of 15:02, 17 August 2022
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	\equiv \langle \beta_{lm}^{\alpha}\|S\|\psi_{n\mathbf{k}}\rangle		\equiv \langle \beta_{lm}^{\alpha}\|S\|\psi_{n\mathbf{k}}\rangle
	= \underbrace{\langle \beta_{lm}^{\alpha}\|\psi_{n\mathbf{k}}\rangle}_{P^{\text{SOFT},\alpha}_{lmn\mathbf{k}}} +		= \underbrace{\langle \beta_{lm}^{\alpha}\|\psi_{n\mathbf{k}}\rangle}_{P^{\text{SOFT},\alpha}_{lmn\mathbf{k}}} +
	\underbrace{\sum_{ij} \langle \beta^\alpha_{lm}\|~~p_i~~\rangle Q_{ij} \langle ~~p_j~~ \| \psi_{n\mathbf{k}}\rangle}_{P^{\text{AUG},\alpha}_{lmn\mathbf{k}}}.		\underbrace{\sum_{ij} \langle \beta^\alpha_{lm}\|\tilde{p}_i\rangle Q_{ij} \langle \tilde{p}_j \| \psi_{n\mathbf{k}}\rangle}_{P^{\text{AUG},\alpha}_{lmn\mathbf{k}}}.
	</math>		</math>

	Here, the two terms on the right-hand side are called soft and augmentation part, respectively, and <math>S</math> is the overlap matrix,		Here, the two terms on the right-hand side are called soft and augmentation part, respectively, and <math>S</math> is the overlap matrix,

	<math>S = 1+\sum_{ij} \|~~p_i~~\rangle Q_{ij} \langle ~~p_j~~\|.</math>		<math>S = 1+\sum_{ij} \|\tilde{p}_i\rangle Q_{ij} \langle \tilde{p}_j\|.</math>

	The radial and the angular part of <math>\beta^\alpha_{lm}(\mathbf{r})</math> are described by a linear combination of spherical bessel functions <math>\phi_n(r)</math> and by spherical harmonics <math>Y^\alpha_{lm}(\hat{\mathbf{r}})</math>, respectively:		The radial and the angular part of <math>\beta^\alpha_{lm}(\mathbf{r})</math> are described by a linear combination of spherical bessel functions <math>\phi_n(r)</math> and by spherical harmonics <math>Y^\alpha_{lm}(\hat{\mathbf{r}})</math>, respectively:

Huebsch: /* Format */

2021-11-29T13:38:16Z

Format

← Older revision		Revision as of 13:38, 29 November 2021
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	*below : augmentation part		*below : augmentation part
	*last line: real part of <math>P^{\text{AUG},\alpha}_{lmn\mathbf{k}}</math> for every <math>lm</math>-quantum number (inner loop), ion per type, ion type, band and k point (outer loop).		*last line: real part of <math>P^{\text{AUG},\alpha}_{lmn\mathbf{k}}</math> for every <math>lm</math>-quantum number (inner loop), ion per type, ion type, band and k point (outer loop).
	{{NB\|warning\|~~This file~~ is not correctly written when {{TAG\|LNONCOLLINEAR}} {{=}} .~~TRUE. for versions of VASP <{{=}} 6.2.1~~ }}		{{NB\|warning\|For VASP version <{{=}} 6.2.1, {{FILE\|PROOUT}} is not correctly written when {{TAG\|LNONCOLLINEAR}} {{=}} True. }}

	== Related Tags and Sections ==		== Related Tags and Sections ==

Huebsch at 13:35, 29 November 2021

2021-11-29T13:35:05Z

← Older revision		Revision as of 13:35, 29 November 2021
Line 5:		Line 5:
	\equiv \langle \beta_{lm}^{\alpha}\|S\|\psi_{n\mathbf{k}}\rangle		\equiv \langle \beta_{lm}^{\alpha}\|S\|\psi_{n\mathbf{k}}\rangle
	= \underbrace{\langle \beta_{lm}^{\alpha}\|\psi_{n\mathbf{k}}\rangle}_{P^{\text{SOFT},\alpha}_{lmn\mathbf{k}}} +		= \underbrace{\langle \beta_{lm}^{\alpha}\|\psi_{n\mathbf{k}}\rangle}_{P^{\text{SOFT},\alpha}_{lmn\mathbf{k}}} +
	\underbrace{\sum_{ij} \langle \beta^\alpha_{lm}\|p_i\rangle Q_{ij} \langle p_j \| \~~phi_~~{n\mathbf{k}}\rangle}_{P^{\text{AUG},\alpha}_{lmn\mathbf{k}}}.		\underbrace{\sum_{ij} \langle \beta^\alpha_{lm}\|p_i\rangle Q_{ij} \langle p_j \| \psi_{n\mathbf{k}}\rangle}_{P^{\text{AUG},\alpha}_{lmn\mathbf{k}}}.
	</math>		</math>

Huebsch at 11:54, 29 November 2021

2021-11-29T11:54:44Z

← Older revision		Revision as of 11:54, 29 November 2021
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	This file is written ~~when~~ {{TAG\|LORBIT}}=5 and {{TAG\|RWIGS}} ~~tags are~~ set in the {{TAG\|INCAR}} file ~~and~~ contains the projection of the ~~Bloch wavefunctions~~ <math>\|\psi_{n\mathbf{k}}\rangle</math> onto <math>\|\beta^\alpha_{lm}\rangle</math> which can be written as		This file is written if {{TAG\|LORBIT}}=5 and the {{TAG\|RWIGS}} tag is set in the {{TAG\|INCAR}} file. It contains the projection of the Kohn-Sham orbitals <math>\|\psi_{n\mathbf{k}}\rangle</math> onto a localized orbitals basis <math>\|\beta^\alpha_{lm}\rangle</math> which can be written as

	<math>		<math>
Line 5:		Line 5:
	\equiv \langle \beta_{lm}^{\alpha}\|S\|\psi_{n\mathbf{k}}\rangle		\equiv \langle \beta_{lm}^{\alpha}\|S\|\psi_{n\mathbf{k}}\rangle
	= \underbrace{\langle \beta_{lm}^{\alpha}\|\psi_{n\mathbf{k}}\rangle}_{P^{\text{SOFT},\alpha}_{lmn\mathbf{k}}} +		= \underbrace{\langle \beta_{lm}^{\alpha}\|\psi_{n\mathbf{k}}\rangle}_{P^{\text{SOFT},\alpha}_{lmn\mathbf{k}}} +
	\underbrace{\sum_{ij} \langle \beta^\alpha_{lm}\|p_i\rangle Q_{ij} \langle p_j \| \~~psi_~~{n\mathbf{k}}\rangle}_{P^{\text{AUG},\alpha}_{lmn\mathbf{k}}}		\underbrace{\sum_{ij} \langle \beta^\alpha_{lm}\|p_i\rangle Q_{ij} \langle p_j \| \phi_{n\mathbf{k}}\rangle}_{P^{\text{AUG},\alpha}_{lmn\mathbf{k}}}.
	</math>		</math>

	~~with~~ the two terms on the right-hand side ~~being~~ called soft and augmentation part respectively and S the overlap matrix		Here, the two terms on the right-hand side are called soft and augmentation part, respectively, and <math>S</math> is the overlap matrix,

	<math>S = 1+\sum_{ij} \|p_i\rangle Q_{ij} \langle p_j\|.</math>		<math>S = 1+\sum_{ij} \|p_i\rangle Q_{ij} \langle p_j\|.</math>

	The angular part of ~~the functions~~ <math>\beta^\alpha_{lm}(\mathbf{r})</math> is described by spherical harmonics <math>Y^\alpha_{lm}(\hat{\mathbf{r}})</math> ~~and the radial part by a linear combination of spherical bessel functions parametrized to be non-zero within a radius determined by {{TAG\|RWIGS}}~~		The radial and the angular part of <math>\beta^\alpha_{lm}(\mathbf{r})</math> are described by a linear combination of spherical bessel functions <math>\phi_n(r)</math> and by spherical harmonics <math>Y^\alpha_{lm}(\hat{\mathbf{r}})</math>, respectively:

	<math>		<math>
Line 19:		Line 19:
	</math>		</math>

	It so happens that ~~the~~ <math>\|p_i\rangle</math> ~~functions have~~ a similar ~~structure to~~ <math>\|\beta^\alpha_{lm}\rangle</math> which simplifies the computations above.		The spherical bessel functions <math>\phi_n(r)</math> are parametrized to be non-zero within a radius determined by {{TAG\|RWIGS}}. In addition, it so happens that <math>\|p_i\rangle</math> has a similar form as <math>\|\beta^\alpha_{lm}\rangle</math> which simplifies the computations above.

	~~For~~ the ~~case of spin-polarized~~ {{TAG\|~~ISPIN~~}}~~=2 or noncollinear calculations~~ {{TAG\|~~LNONCOLLINEAR~~}}~~=.TRUE.~~, ~~two files are produced PROOUT.1~~ and ~~PROOUT.2 referring to~~ the ~~up and down~~ part of the ~~spinor of the orbital~~.		The {{TAG\|PROOUT}} file contains similar information as the {{TAG\|PROCAR}} file but the following differences exist:
	{{NB\|~~warning\|This~~ file ~~is not correctly written when~~ {{~~TAG\|LNONCOLLINEAR~~}} {{=}} ~~.TRUE. for versions of VASP~~ <{{=}} 6.2.~~1 }}~~		*The {{TAG\|PROOUT}} file writes the real and imaginary parts of <math>P^{\text{SOFT},\alpha}_{lmn\mathbf{k}}</math>, and the real part of the augmentation part <math>P^{\text{AUG},\alpha}_{lmn\mathbf{k}}</math>.
			The {{TAG\|PROCAR}} file contains the information of the squared projection, <math>P^\alpha_{lmn\mathbf{k}} (P^\alpha_{lmn\mathbf{k}})^{}</math>, whereas the {{TAG\|PROOUT}} file contains <math>P^\alpha_{lmn\mathbf{k}}</math>.
			*The arrangement of the output is very different in both files.

	~~The {{TAG\|PROOUT}} file is similar in~~ information to ~~the {{TAG\|PROCAR}} file but the following differences exist:~~		This information makes it possible to construct, e.g., partial DOS projected onto bonding and anti-bonding molecular orbitals and the so-called crystal-orbital-overlap-population (COOP) function. Depending on the application, users might find it more practical to use the information contained in the {{FILE\|PROJCAR}} and {{FILE\|LOCPROJ}} files. These are controlled by the {{TAG\|LOCPROJ}} tag.
	*The {{TAG\|PROOUT}} file writes the real and ~~imaginary parts of <math>P^{\text{SOFT},\alpha}_{lmn\mathbf{k}}</math>~~ and the ~~real part of~~ the ~~augmentation part <math>P^{\text{AUG}~~,~~\alpha}_{lmn\mathbf{k}}</math>.~~
	The {{TAG\|PROCAR}} file contains the information on the ~~square, <math>P^\alpha_~~{~~lmn\mathbf~~{k}} ~~(P^\alpha_~~{~~lmn\mathbf~~{k}}~~)^{}</math>, whereas~~ the {{TAG\|~~PROOUT~~}} ~~file describes <math>P^\alpha_{lmn\mathbf{k}}</math>.~~
	*The arrangement of the output is very different in both files.

	~~Depending on the intended application users might find it more practical to use the information contained in the~~ {{~~FILE~~\|~~PROJCAR~~}} and {{~~FILE~~\|~~LOCPROJ~~}} ~~files controlled by~~ the ~~{{TAG\|LOCPROJ}} tag~~.		For spin-polarized calculations with {{TAG\|ISPIN}}=2 and noncollinear calculations with {{TAG\|LNONCOLLINEAR}}=.TRUE., '''PROOUT.1''' and '''PROOUT.2''' are written, referring to the Kohn-Sham orbitals' two spin components.

	== Format ==		== Format ==
Line 35:		Line 34:
	*line 2: Number of kpoints, bands and ions		*line 2: Number of kpoints, bands and ions
	*line 3: Twice the number of types followed by the number of ions for each type		*line 3: Twice the number of types followed by the number of ions for each type
	*line 4: The Fermi weights for each ~~kpoint~~ (inner loop) and band (outer loop)		*line 4: The Fermi weights for each k point (inner loop) and band (outer loop)
	*line 5 <math>-</math> ...: Real and imaginary part of <math>P^{\text{SOFT},\alpha}_{lmn\mathbf{k}}</math> for every lm-quantum number (inner loop), band, ion per type, ~~kpoint~~ and ion-type (outer loop)		*line 5 <math>-</math> ...: Real and imaginary part of <math>P^{\text{SOFT},\alpha}_{lmn\mathbf{k}}</math> for every <math>lm</math>-quantum number (inner loop), band, ion per type, k point and ion type (outer loop).
	*below : augmentation part		*below : augmentation part
	*last line: real part of <math>P^{\text{AUG},\alpha}_{lmn\mathbf{k}}</math> for every lm-quantum number (inner loop), ion per type, ion-type, band and k point (outer loop)		*last line: real part of <math>P^{\text{AUG},\alpha}_{lmn\mathbf{k}}</math> for every <math>lm</math>-quantum number (inner loop), ion per type, ion type, band and k point (outer loop).
			{{NB\|warning\|This file is not correctly written when {{TAG\|LNONCOLLINEAR}} {{=}} .TRUE. for versions of VASP <{{=}} 6.2.1 }}
	This ~~information makes it possible to construct e~~.g. ~~partial DOS projected onto bonding and anti-bonding molecular orbitals or the so-called coop (crystal overlap population function)~~.

	== Related Tags and Sections ==		== Related Tags and Sections ==
	{{TAG\|LORBIT}} {{FILE\|LOCPROJ}} {{FILE\|PROJCAR}}		{{TAG\|LORBIT}}, {{FILE\|LOCPROJ}}, {{FILE\|PROJCAR}}, {{FILE\|PROCAR}}

	----		----

	[[Category:Files]][[Category:Output Files]]		[[Category:Files]][[Category:Output Files]]

Miranda.henrique at 11:27, 29 November 2021

2021-11-29T11:27:41Z

← Older revision		Revision as of 11:27, 29 November 2021
Line 21:		Line 21:
	It so happens that the <math>\|p_i\rangle</math> functions have a similar structure to <math>\|\beta^\alpha_{lm}\rangle</math> which simplifies the computations above.		It so happens that the <math>\|p_i\rangle</math> functions have a similar structure to <math>\|\beta^\alpha_{lm}\rangle</math> which simplifies the computations above.

	For the case of spin-polarized {{TAG\|ISPIN}}=2 or noncollinear calculations {{TAG\|LNONCOLLINEAR}}=.TRUE., two files are produced ~~PROCAR~~.1 and ~~PROCAR~~.2 referring to the up and down part of the spinor of the orbital.		For the case of spin-polarized {{TAG\|ISPIN}}=2 or noncollinear calculations {{TAG\|LNONCOLLINEAR}}=.TRUE., two files are produced PROOUT.1 and PROOUT.2 referring to the up and down part of the spinor of the orbital.
	{{NB\|warning\|This file is not correctly written when {{TAG\|LNONCOLLINEAR}} {{=}} .TRUE. for versions of VASP <{{=}} 6.2.1 }}		{{NB\|warning\|This file is not correctly written when {{TAG\|LNONCOLLINEAR}} {{=}} .TRUE. for versions of VASP <{{=}} 6.2.1 }}

Miranda.henrique at 11:26, 29 November 2021

2021-11-29T11:26:27Z

← Older revision		Revision as of 11:26, 29 November 2021
Line 1:		Line 1:
	This file is written when {{TAG\|LORBIT}}=5 and {{TAG\|RWIGS}} tags are set in the {{TAG\|INCAR}} file and contains the projection of the wavefunctions <math>\|\~~phi_~~{n\mathbf{k}}\rangle</math> onto <math>\|\beta^\alpha_{lm}\rangle</math> which can be written as		This file is written when {{TAG\|LORBIT}}=5 and {{TAG\|RWIGS}} tags are set in the {{TAG\|INCAR}} file and contains the projection of the Bloch wavefunctions <math>\|\psi_{n\mathbf{k}}\rangle</math> onto <math>\|\beta^\alpha_{lm}\rangle</math> which can be written as

	<math>		<math>
	P^\alpha_{lmn\mathbf{k}}		P^\alpha_{lmn\mathbf{k}}
	\equiv \langle \beta_{lm}^{\alpha}\|S\|\~~phi_~~{n\mathbf{k}}\rangle		\equiv \langle \beta_{lm}^{\alpha}\|S\|\psi_{n\mathbf{k}}\rangle
	= \underbrace{\langle \beta_{lm}^{\alpha}\|\~~phi_~~{n\mathbf{k}}\rangle}_{P^{\text{SOFT},\alpha}_{lmn\mathbf{k}}} +		= \underbrace{\langle \beta_{lm}^{\alpha}\|\psi_{n\mathbf{k}}\rangle}_{P^{\text{SOFT},\alpha}_{lmn\mathbf{k}}} +
	\underbrace{\sum_{ij} \langle \beta^\alpha_{lm}\|p_i\rangle Q_{ij} \langle p_j \| \~~phi_~~{n\mathbf{k}}\rangle}_{P^{\text{AUG},\alpha}_{lmn\mathbf{k}}}		\underbrace{\sum_{ij} \langle \beta^\alpha_{lm}\|p_i\rangle Q_{ij} \langle p_j \| \psi_{n\mathbf{k}}\rangle}_{P^{\text{AUG},\alpha}_{lmn\mathbf{k}}}
	</math>		</math>

Miranda.henrique at 13:57, 23 November 2021

2021-11-23T13:57:46Z

← Older revision		Revision as of 13:57, 23 November 2021
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	The {{TAG\|PROCAR}} file contains the information on the square, <math>P^\alpha_{lmn\mathbf{k}} (P^\alpha_{lmn\mathbf{k}})^{}</math>, whereas the {{TAG\|PROOUT}} file describes <math>P^\alpha_{lmn\mathbf{k}}</math>.		The {{TAG\|PROCAR}} file contains the information on the square, <math>P^\alpha_{lmn\mathbf{k}} (P^\alpha_{lmn\mathbf{k}})^{}</math>, whereas the {{TAG\|PROOUT}} file describes <math>P^\alpha_{lmn\mathbf{k}}</math>.
	*The arrangement of the output is very different in both files.		*The arrangement of the output is very different in both files.

			Depending on the intended application users might find it more practical to use the information contained in the {{FILE\|PROJCAR}} and {{FILE\|LOCPROJ}} files controlled by the {{TAG\|LOCPROJ}} tag.

	== Format ==		== Format ==
Line 39:		Line 41:

	This information makes it possible to construct e.g. partial DOS projected onto bonding and anti-bonding molecular orbitals or the so-called coop (crystal overlap population function).		This information makes it possible to construct e.g. partial DOS projected onto bonding and anti-bonding molecular orbitals or the so-called coop (crystal overlap population function).

			== Related Tags and Sections ==
			{{TAG\|LORBIT}} {{FILE\|LOCPROJ}} {{FILE\|PROJCAR}}

	----		----

	[[Category:Files]][[Category:Output Files]]		[[Category:Files]][[Category:Output Files]]

Miranda.henrique at 10:50, 23 November 2021

2021-11-23T10:50:48Z

← Older revision		Revision as of 10:50, 23 November 2021
Line 1:		Line 1:
	This file contains the projection of the wavefunctions <math>\|\phi_{n\mathbf{k}}\rangle</math> onto <math>\|\beta^\alpha_{lm}\rangle</math>		This file is written when {{TAG\|LORBIT}}=5 and {{TAG\|RWIGS}} tags are set in the {{TAG\|INCAR}} file and contains the projection of the wavefunctions <math>\|\phi_{n\mathbf{k}}\rangle</math> onto <math>\|\beta^\alpha_{lm}\rangle</math> which can be written as

	<math>		<math>
Line 10:		Line 10:
	with the two terms on the right-hand side being called soft and augmentation part respectively and S the overlap matrix		with the two terms on the right-hand side being called soft and augmentation part respectively and S the overlap matrix

	<math>S = 1+\sum_{ij} \|p_i\rangle Q_{ij} \langle p_j\|</math>		<math>S = 1+\sum_{ij} \|p_i\rangle Q_{ij} \langle p_j\|.</math>

	The angular part of the functions <math>\beta^\alpha_{lm}(\mathbf{r})</math> is described by spherical harmonics <math>Y^\alpha_{lm}(\hat{\mathbf{r}})</math> and the radial part by a linear combination of spherical bessel functions parametrized to be non-zero within a radius determined by {{TAG\|RWIGS}}.		The angular part of the functions <math>\beta^\alpha_{lm}(\mathbf{r})</math> is described by spherical harmonics <math>Y^\alpha_{lm}(\hat{\mathbf{r}})</math> and the radial part by a linear combination of spherical bessel functions parametrized to be non-zero within a radius determined by {{TAG\|RWIGS}}

	<math>		<math>
	\beta^\alpha_{lm}(\mathbf{r}) =		\beta^\alpha_{lm}(\mathbf{r}) =
	Y^\alpha_{lm}(\hat{\mathbf{r}})\sum_n \phi_n(r)		Y^\alpha_{lm}(\hat{\mathbf{r}})\sum_n \phi_n(r).
	</math>		</math>

	it so happens that the <math>\|p_i\rangle</math> functions have a similar structure to <math>\|\beta^\alpha_{lm}\rangle</math> which simplifies the computations above.		It so happens that the <math>\|p_i\rangle</math> functions have a similar structure to <math>\|\beta^\alpha_{lm}\rangle</math> which simplifies the computations above.

	~~Available from VASP version 3~~.2 and ~~upwards~~.		For the case of spin-polarized {{TAG\|ISPIN}}=2 or noncollinear calculations {{TAG\|LNONCOLLINEAR}}=.TRUE., two files are produced PROCAR.1 and PROCAR.2 referring to the up and down part of the spinor of the orbital.
			{{NB\|warning\|This file is not correctly written when {{TAG\|LNONCOLLINEAR}} {{=}} .TRUE. for versions of VASP <{{=}} 6.2.1 }}
	~~The~~ {{~~TAG~~\|~~PROOUT}}~~ file is ~~only~~ written ~~out if the~~ {{TAG\|~~LORBIT~~}}~~=5 flag is set with an appropriate~~ {{~~TAG\|RWIGS~~}} ~~flag in the~~ {{~~TAG\|INCAR~~}} ~~file~~.

	The {{TAG\|PROOUT}} file is similar in information to the {{TAG\|PROCAR}} file but the following differences exist:		The {{TAG\|PROOUT}} file is similar in information to the {{TAG\|PROCAR}} file but the following differences exist:
Line 40:		Line 39:

	This information makes it possible to construct e.g. partial DOS projected onto bonding and anti-bonding molecular orbitals or the so-called coop (crystal overlap population function).		This information makes it possible to construct e.g. partial DOS projected onto bonding and anti-bonding molecular orbitals or the so-called coop (crystal overlap population function).

	~~{{NB\|warning\|This file is not correctly written when {{TAG\|LNONCOLLINEAR}} {{=}} .TRUE. for versions of VASP <{{=}} 6.2.1 }}~~

	----		----

	[[Category:Files]][[Category:Output Files]]		[[Category:Files]][[Category:Output Files]]

← Older revision		Revision as of 11:27, 29 November 2021
Line 21:		Line 21:
	It so happens that the <math>\|p_i\rangle</math> functions have a similar structure to <math>\|\beta^\alpha_{lm}\rangle</math> which simplifies the computations above.		It so happens that the <math>\|p_i\rangle</math> functions have a similar structure to <math>\|\beta^\alpha_{lm}\rangle</math> which simplifies the computations above.

	For the case of spin-polarized {{TAG\|ISPIN}}=2 or noncollinear calculations {{TAG\|LNONCOLLINEAR}}=.TRUE., two files are produced ~~PROCAR~~.1 and ~~PROCAR~~.2 referring to the up and down part of the spinor of the orbital.		For the case of spin-polarized {{TAG\|ISPIN}}=2 or noncollinear calculations {{TAG\|LNONCOLLINEAR}}=.TRUE., two files are produced PROOUT.1 and PROOUT.2 referring to the up and down part of the spinor of the orbital.
	{{NB\|warning\|This file is not correctly written when {{TAG\|LNONCOLLINEAR}} {{=}} .TRUE. for versions of VASP <{{=}} 6.2.1 }}		{{NB\|warning\|This file is not correctly written when {{TAG\|LNONCOLLINEAR}} {{=}} .TRUE. for versions of VASP <{{=}} 6.2.1 }}